Temporal splitting algorithms for non-stationary multiscale problems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:439

Article

Efendiev, Yalchin^1,2  Pun, Sai-Mang¹  Vabishchevich, Petr N.^2,3 

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[2] North Eastern Fed Univ, Yakutsk, Russia

[3] Russian Acad Sci, Nucl Safety Inst, Moscow, Russia

关键词: Multiscale;    GMsFEM;    Splitting;    Porous media;    Three-layer;   

DOI  :  10.1016/j.jcp.2021.110375

来源: Elsevier

【 摘 要 】

In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale details on a coarse grid and, thus, reduce the problems' size. When solving time-dependent problems, one can take advantage of the multiscale decomposition of the solution and perform temporal splitting by solving smaller-dimensional problems, which is studied in the paper. In the proposed approach, we consider the temporal splitting based on various low dimensional spatial approximations. Because a multiscale spatial splitting gives a good decomposition of the solution space, one can achieve an efficient implicit-explicit temporal discretization. We present a recently developed theoretical result in [15] and adopt in this paper for multiscale problems. Numerical results are presented to demonstrate the efficiency of the proposed splitting algorithm. (C) 2021 Published by Elsevier Inc.

【 授权许可】

Free